One end of a taut string of length `3m` along the x-axis is fixed at `x = 0`. The speed of the waves in the string is `100ms^(-1)`. The other end of the string is vibrating in the y-direction so that stationary waves are set up in the string. The possible wavelength`(s)` of these sationary waves is (are)

Options

A. (a) `y(t) = A sin(pix)/(6)cos(50pit)/(3)`
B. (b) `y(t) = A sin(pix)/(3)cos(100pit)/(3)`
C. ( c ) `y(t) = A sin(5pix)/(6)cos(250pit)/(3)`
D. (d) `y(t) = A sin(5pix)/(2)cos 250pit`

Answer

A, C, D

Explanation

(a,c,d) Clearly in the given situation a displacement node is present at `x = 0` and `a` displacement antitode is present at `x = 3m`.
The velocity `v = (omega)/(k) = 100ms^(-1)`.
`a , c and d` are the coerrct option which satisfy the above conditions.